What does the button next to the Pivot Point button do?
That button  is the manipulate center points option, which allows you to manipulate the origins of objects without affecting the rotation and scale of the objects themselves.

For example, if I scale these objects without it enabled, they are stretched. With it enabled, only the origins are moved (only affecting object location):



Note that with only one object selected, enabling this option will cause scaling or rotating the object to do nothing.